A200677 Smallest semiprime such that the sum of the two prime factors equals n, or zero if impossible.

0, 0, 0, 4, 6, 9, 10, 15, 14, 21, 0, 35, 22, 33, 26, 39, 0, 65, 34, 51, 38, 57, 0, 95, 46, 69, 0, 115, 0, 161, 58, 87, 62, 93, 0, 155, 0, 217, 74, 111, 0, 185, 82, 123, 86, 129, 0, 215, 94, 141, 0, 235, 0, 329, 106, 159, 0, 265, 0, 371, 118, 177, 122, 183, 0

Offset

1,4

Comments

For n > 3, a(n) = 0 if n-2 is an odd composite.

The sequence without zeros is a subsequence of A189553. - Manfred Scheucher, Aug 08 2015

The two prime factors are not necessarily distinct; a(6) = 9, both of whose prime factors are 3s. - Jon E. Schoenfield, Aug 09 2015

Links

Table of n, a(n) for n=1..65.

Formula

a(A014091(n)) > 0; a(A014092(n)) = 0. - Michel Marcus, Aug 10 2015

Example

a(10) = 21 because 21 = 3*7 and 3+7 = 10, and there is no semiprime smaller than 21 whose two prime factors sum to 10.

Maple

with(numtheory):for n from 1 to 65 do:ii:=0:for k from 1 to 1000 while(ii=0)do:m1:=bigomega(k):x:=factorset(k): m2:=nops(x):if m1=2 and m2=2 and x[1]+x[2]= n or m1=2 and m2=1 and 2*x[1]= n then ii:=1: printf(`%d, `, k):else fi:od:if ii=0 then printf(`%d, `, 0):else fi:od:

Crossrefs

Cf. A001358, A014091, A014092, A135093.

Sequence in context: A318990 A132435 A108631 * A189553 A189482 A099303

Adjacent sequences: A200674 A200675 A200676 * A200678 A200679 A200680

Keyword

nonn

Author

Michel Lagneau, Nov 20 2011

Extensions

Edited by Jon E. Schoenfield and Manfred Scheucher, Aug 09 2015

Status

approved